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3 years ago

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A sector of a circle has a central angle measuring 15 degrees and the radius of the circle measures 9 inches. What is the arc le

ngth of the sector? Express the answer in terms of Pi.
Recall that StartFraction Arc length over Circumference EndFraction = StartFraction n degrees over 360 degrees EndFraction.
StartFraction 3 over 8 EndFraction pi inches
Three-fourths pi inches
1 and StartFraction 3 over 8 EndFraction pi inches
1 and one-half pi inches

1 answer:

Kamila [148]3 years ago

5 0

Answer:

Arc length is $\dfrac{3\pi }{4}\ \text{inches}$

Step-by-step explanation:

We have,

Central angle is 15 degrees and the radius of the circle measures 9 inches.

It is required to find the arc length of the sector.

The relation between arc length and the central angle is given by :

$\dfrac{\text{arc length}}{\text{circumference}}=\dfrac{\theta}{360}$

Circumference, $C=2\pi r=18\pi$

$\theta=15^{\circ}$

$\dfrac{x}{18\pi }=\dfrac{15}{360}\\\\\dfrac{x}{18\pi }=\dfrac{1}{24}\\\\x=\dfrac{18\pi }{24}\\\\x=\dfrac{3\pi }{4}\ \text{inches}$

Hence, the correct option is (b).

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A gardener buys a rake and a pair of gloves for each of the 12 volunteers in the gardening club. Each pair of gloves

matrenka [14]

Let unit cost of one rake be : r

Given : Total number of volunteers = 12

Given : Each pair of gloves cost $8.00

⇒ Cost of 12 pair of gloves for 12 volunteers = (12 × 8) = $96

Given : The gardener spends a total of $300 on both rakes and gloves

⇒ Cost of 12 rakes + Cost of 12 pair of gloves = $300

⇒ 12r + 96 = 300

⇒ 12r = 204

⇒ r = 17

<u>Answer</u> : Cost of one rake is $17

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3 years ago

You have a wire that is 38 cm long. you wish to cut it into two pieces. one piece will be bent into the shape of a square. the o

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Circumference + perimeter =38
x = circumference of circle
find r in terms of x
2 $\pi$ r=x
r= $\frac{x}{2 \pi }$
Area= $\pi$ r^2
so..
A= $\pi$ ( $\frac{x}{2 \pi }$ )^2
= $\pi$ ( $\frac{x^{2} }{4 \pi ^{2} }$ )
= $\frac{x^{2} }{4 \pi }$

(38-x) is perimeter
then
$\frac{38-x}{4}$
( $\frac{38-x}{4}$ )^2
$\frac{x^{2} }{4 \pi }$ + ( $\frac{38-x}{4}$ )^2
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3 years ago

company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 26

podryga [215]

Answer:

$t=\frac{25.02-26}{\frac{4.83}{\sqrt{50}}}=-1.435$

$p_v =P(t_{(49)}$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant lower than 26 so then the specification is satisfied.

Step-by-step explanation:

Data given and notation

$\bar X=25.02$ represent the sample mean

$s=4.83$ represent the sample standard deviation

$n=50$ sample size

$\mu_o =26$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is at least 26 mpg, the system of hypothesis would be:

Null hypothesis: $\mu \geq 26$

Alternative hypothesis: $\mu < 26$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{25.02-26}{\frac{4.83}{\sqrt{50}}}=-1.435$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=50-1=49$

Since is a one sided test the p value would be:

$p_v =P(t_{(49)}$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant lower than 26 so then the specification is satisfied.

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3 years ago

PLEASE HELP ILL THANK U AND RATE

MrRa [10]

Since u need the surface area of a rectangular prism it is length•width•height so the answer is 24 feet squared

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